An investment portfolio is initially valued at $8.00 dollars. During the first quarter, its value increases to 285% of the...
GMAT Problem-Solving and Data Analysis : (PS_DA) Questions
An investment portfolio is initially valued at \(\$8.00\) dollars. During the first quarter, its value increases to \(285\%\) of the initial value. During the second quarter, its value decreases to \(30\%\) of the value at the end of the first quarter. What is the value of the investment portfolio at the end of the second quarter, in dollars?
Express your answer as a decimal to the nearest hundredth.
1. TRANSLATE the problem information
- Given information:
- Initial portfolio value: \(\$8.00\)
- First quarter: increases to 285% of initial value
- Second quarter: decreases to 30% of value at end of first quarter
- What this tells us: We need two sequential percentage calculations
2. INFER the approach
- This is a sequential calculation problem - the result from the first quarter becomes the starting point for the second quarter
- "285% of" means multiply by 2.85 (since \(285\% = 285/100 = 2.85\))
- "30% of" means multiply by 0.30 (since \(30\% = 30/100 = 0.30\))
3. SIMPLIFY the first quarter calculation
- Value after first quarter = Initial value × 2.85
- Value after first quarter = \(\$8.00 \times 2.85 = \$22.80\)
4. SIMPLIFY the second quarter calculation
- Value after second quarter = First quarter result × 0.30
- Value after second quarter = \(\$22.80 \times 0.30 = \$6.84\)
Answer: 6.84
Why Students Usually Falter on This Problem
Most Common Error Path:
Weak TRANSLATE skill: Students misinterpret "increases to 285%" as meaning "increases BY 285%" (adding 285% rather than setting equal to 285%).
This leads them to calculate: \(8.00 + (8.00 \times 2.85) = 8.00 + 22.80 = 30.80\) for the first quarter, then \(30.80 \times 0.30 = 9.24\) for the final answer. This causes confusion since 9.24 doesn't match the expected precision, leading to guessing.
Second Most Common Error:
Poor SIMPLIFY execution: Students make arithmetic errors in the decimal multiplication, particularly with \(8.00 \times 2.85\) or \(22.80 \times 0.30\).
Common calculation mistakes include getting 22.8 instead of 22.80, or 6.8 instead of 6.84. This leads to answers that are close but don't match the required precision to the nearest hundredth, causing them to second-guess their work and potentially guess.
The Bottom Line:
This problem tests whether students can correctly interpret percentage language and execute sequential calculations. The key insight is recognizing that "increases to 285%" means the new value equals 285% of the original, not that you add 285% to the original.